Astronomy&
Astrophysics

A&A 555, A139 (2013)
DOI: 10.1051/0004-6361/201220830
c ESO 2013
High-rigidity Forbush decreases: due to CMEs or shocks?
K. P. Arunbabu1 , H. M. Antia2,3 , S. R. Dugad2,3 , S. K. Gupta2,3 , Y. Hayashi4 , S. Kawakami4 , P. K. Mohanty2,3 ,T. Nonaka4 , A. Oshima5 , and P. Subramanian1(The GRAPES-3 Collaboration)
1

Indian Institute of Science Education and Research, Sai Trinity Building, Pashan, 411 021 Pune, India
Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005 Mumbai, India
3
The GRAPES–3 Experiment, Cosmic Ray Laboratory, Raj Bhavan, 643 001 Ooty, India
4
Graduate School of Science, Osaka City University, 558-8585 Osaka, Japan
5
National Astronomical Observatory of Japan, CfCA, 181-8588 Tokyo, Japan
2

Received 2 December 2012 / Accepted 17 April 2013
ABSTRACT

Aims. We seek to identify the primary agents causing Forbush decreases (FDs) in high-rigidity cosmic rays observed from the Earth.
In particular, we ask if these FDs are caused mainly by coronal mass ejections (CMEs) from the Sun that are directed towards the
Earth, or by their associated shocks.
Methods. We used the muon data at cutoﬀ rigidities ranging from 14 to 24 GV from the GRAPES-3 tracking muon telescope toidentify FD events. We selected those FD events that have a reasonably clean profile, and can be reasonably well associated with an
Earth-directed CME and its associated shock. We employed two models: one that considers the CME as the sole cause of the FD (theCME-only model) and one that considers the shock as the only agent causing the FD (the shock-only model). We used an extensive setof observationally determined parameters for both models. The only free parameter in these models is the level of MHD turbulence inthe sheath region, which mediates cosmic ray diﬀusion (into the CME for the CME-only model, and across the shock sheath for theshock-only model).
Results. We find that good fits to the GRAPES-3 multi-rigidity data using the CME-only model require turbulence levels in the CME
sheath region that are only slightly higher than those estimated for the quiescent solar wind. On the other hand, reasonable model fitswith the shock-only model require turbulence levels in the sheath region that are an order of magnitude higher than those in the quiet
solar wind.
Conclusions. This observation naturally leads to the conclusion that the Earth-directed CMEs are the primary contributors to FDs
observed in high-rigidity cosmic rays.
Key words. Sun: coronal mass ejections (CMEs) – cosmic rays

1. Introduction
Forbush decreases (FDs) are short-term decreases in the intensity of the Galactic cosmic rays observed from the Earth. They
are typically caused by the eﬀects of interplanetary counterpartsof coronal mass ejections (CMEs) from the Sun, and also the
corotating interaction regions (CIRs) between the fast and slow
solar wind streams from the Sun. We concentrate on CME driven
FDs in this paper. The near-Earth manifestations of CMEs fromthe Sun typically have two major components: the interplanetary
counterpart of the CME, commonly called an ICME, and theshock which is driven ahead of it. ICMEs which possess certain
well-defined criteria such as reductions in plasma temperatureand smooth rotations of the magnetic field (e.g., Burlaga et al.
1981; Bothmer & Schwenn 1998) are called magnetic clouds,
while others are often classified as ejecta. The relative contributions of shocks and ICMEs in causing FDs is a matter of debate. For instance, Zhang & Burlaga (1988), Lockwood et al.
(1991), and Reames et al. (2009) argue against the contribution of magnetic clouds to FDs. On the other hand, other studies(e.g., Badruddin et al. 1986; Sanderson et al. 1990; Kuwabara
et al. 2009) have concluded that magnetic clouds can make anAppendix A is available in electronic form at
http://www.aanda.org

important contribution to FDs. There have been recent conclusive associations of FDs with Earth-directed CMEs (Blanco et al.
2013; Oh & Yi 2012). Cane (2000) introduced the concept of a
two-step FD, where the first step of the decrease is due to theshock and the second step is due to the ICME. Based on an extensive study of ICME-associated FDs at cosmic ray energies
between 0.5–450 MeV, Richardson & Cane (2011) conclude thatshock and ICME eﬀects are equally responsible for the FD. They
also find that ICMEs that can be classified as magnetic clouds
are usually involved in the largest of the FDs they studied. From
now on, we will use the term CME to denote the CME near theSun, as well as its counterpart observed from the Earth.
In this paper we have used FD data from the GRAPES-3
tracking muon telescope located at Ooty (11.4◦N latitude,
76.7◦E longitude, and 2200 m altitude) in south India. The
GRAPES-3 muon telescope records the flux of muons in nine
independent directions (labeled NW, N, NE, W, V, E, SW, S
and SE), and the geomagnetic cutoﬀ rigidity over this field ofview varies from 12 to 42 GV. The details of this telescope are
discussed in Hayashi et al. (2005), Nonaka et al. (2006), andSubramanian et al. (2009). Thus, the GRAPES-3 telescope observes the cosmic ray muon flux in nine independent directions
with varying cutoﬀ rigidities simultaneously. The high muoncounting rate measured by the GRAPES-3 telescope results in
extremely small statistical errors, allowing small changes in the

Article published by EDP Sciences

A139, page 1 of 11

A&A 555, A139 (2013)

2. Criteria for shortlisting events
2.1. First and second shortlists: characteristics of the FD

Fig. 1. A schematic of the CME-shock system. The CME is modeled
as a flux rope structure. The undulating lines ahead of the shock denote
MHD turbulence driven by the shock, while those in the CME sheathregion denote turbulence in that region.

We have examined all FD events observed by the GRAPES-3
muon telescope from 2001 to 2004. We then shortlisted events
that have magnitudes >0.25% and possess a relatively clean
profile comprising a sudden decrease followed by a gradualexponential recovery. While the figure of 0.25% might seemrather small by neutron monitor standards, we emphasize thatthe largest events observed with GRAPES-3 have magnitudes of∼1%. This list, which contains 72 events, is called shortlist 1.
We next correlate the events in shortlist 1 with lists of magnetic
clouds near the Earth observed by the WIND and ACE spacecrafts (Huttunen et al. 2005; Lynch et al. 2003; A. Lara, priv.
comm.) and select only those that can be connected reasonably
well with a near-Earth magnetic cloud, and this set is labeledshortlist 2 (Table 1). The decrease minimum for most of the FD
events in shortlist 2 lie between the start and the end of the nearEarth magnetic cloud.
2.2. Third shortlist: CME velocity profile

intensity of the cosmic ray flux to be measured with high precision. Thus a small drop (∼0.2%) in the cosmic ray flux during a FD event can be reliably detected. This is possible even in
the presence of the diurnal anisotropy of much larger magnitude(∼1.0%), through a filtering technique described in Subramanian
et al. (2009) (referred to hereafter as S09).
A schematic of the CME, which is assumed to have a fluxrope geometry (Vourlidas et al. 2012), together with the shock it
drives, is shown in Fig. 1. The shock drives turbulence ahead ofit, and there is also turbulence in the CME sheath region (e.g.,
Manoharan et al. 2000; Richardson & Cane 2011).
Instead of treating the entire system shown in Fig. 1, which
would be rather involved, we consider two separate models. The
first, which we call the CME-only model, is one where the FD
is assumed to be exclusively due to the CME, which is progressively populated by high energy cosmic rays as it propagatesfrom the Sun to the Earth. The preliminary idea behind thismodel was first sketched by Cane et al. (1995) and was further
developed in S09. However, the work we describe here addresses
the multi-rigidity data, which is a major improvement over S09.
We will describe several other salient improvements in the CMEonly model in subsequent sections. The second model, which wecall the shock-only model, is one where the FD is assumed toarise only as a result of a propagating diﬀusive barrier, whichis the shock driven by the CME (e.g., Wibberenz et al. 1998).
The diﬀusive barrier would act as a shield for the Galactic cosmic ray flux, resulting in a lower cosmic ray density behind it.
In treating these two models separately we aim to identify whichis the dominant contributor to the observed FD, the CME, or theshock.
We identify FDs in the GRAPES-3 data that are associatedwith near-Earth magnetic clouds and possibly with the shocks
driven by them. We describe our criteria for shortlisting events inthe next section. We then test the extent to which each of the twomodels satisfies the multi-rigidity FD data from the GRAPES-3
muon telescope. In the subsequent analysis the use of cutoﬀ
rigidity rather than median rigidity is preferred for the following reason. The cutoﬀ rigidity in a given direction represents thethreshold rigidity of incoming cosmic rays and the magnitude of
FD is a sensitive function of it. Instead, the median rigidity iscomparatively insensitive to the magnitude of the FD.
A139, page 2 of 11

Since we are looking for FD events that are associated withshocks as well as CMEs, we examine the CME catalog1 for anear-Sun CME that can reasonably correspond to the near-Earthmagnetic cloud that we associated with the FD in forming shortlist 2. In S09 it was assumed that the CME propagates with aconstant speed from the Sun to the Earth. In this paper, we adopt
a more realistic, two-step velocity profile described below.
The data from the LASCO coronograph aboard the SOHO
spacecraft1 1 provide details about CME propagation up to a distance of ≈30 R from the Sun. We fit the velocity profile to the
LASCO data points
V1 = v i + a i t ,for R(t) ≤ Rm ,(1)

where vi and ai are the initial velocity and acceleration of
CME, respectively, and Rm is the heliocentric distance at which
the CME is last observed in the LASCO field of view. For
distances >Rm , we assume that the CME dynamics are governed exclusively by the aerodynamic drag it experiences due
to momentum coupling with the ambient solar wind. For heliocentric distances >Rm , we therefore use the widely used onedimensional diﬀerential equation to determine the CME velocity
profile: (e.g., Borgazzi et al. 2009)
mCME V2∂V2 1= CD ρsw ACME (V2 − Vsw )2 ,∂R
2R(t) > Rm ,(2)

where mCME is the CME mass, CD is the dimensionless dragcoeﬃcient, ρsw is the solar wind density, ACME = πR2CME is the
cross-sectional area of the CME, and Vsw is the solar wind speed.
The boundary condition used is V2 = vm at R(t) = Rm . The CME
mass mCME is assumed to be 1015 g and the solar wind speed Vsw
is taken to be equal to 450 km s−1 . The solar wind density ρsw
is given by the model of Leblanc et al. (1998). The composite
velocity profile for the CME is defined by
V1 , R(t) ≤ Rm
(3)
VCME =
V2 , R(t) > Rm .
 Rf
The total travel time for the CME is R dR/VCME, where Ri isithe heliocentric radius at which the CME is first detected and1

http://cdaw.gsfc.nasa.gov/CME_list/

K. P. Arunbabu et al.: High-rigidity Forbush decreases
Table 1. Selected events.
Event
Magnitude (%)
2001 Apr. 11
2.86
2001 Aug. 17
1.03
2001 Sep. 29
2.442001 Nov. 24
1.56
2002 May 23
0.93
2002 Sep. 7
0.97
2002 Sep. 30
0.972003 Nov. 20
1.16
2004 Jul. 26
2.13

FD onset (UT)2001 Apr. 11 12:00
2001 Aug. 16 22:34
2001 Sep. 29 12:43
2001 Nov. 24 03:21
2002 May 23 02:10
2002 Sep. 7 14:52
2002 Sep. 30 11:30
2003 Nov. 20 10:48
2004 Jul. 26 15:36

FD min (UT)2001 Apr. 12 18:00
2001 Aug. 18 05:00
2001 Oct. 1 01:00
2001 Nov. 25 15:00
2002 May 23 23:00
2002 Sep. 8 13:00
2002 Oct. 1 08:00
2003 Nov. 24 04:00
2004 Jul. 27 11:00

MC start (UT)2001 Apr. 11 23:00
2001 Aug. 18 00:00
2001 Sep. 29 16:30
2001 Nov. 24 17:00
2002 May 23 21:30
2002 Sep. 7 17:00
2002 Sep. 30 22:00
2003 Nov. 22 06:10
2004 Jul. 27 02:00

MC stop (UT)
CME launch (UT)2001 Apr. 12 18:00 2001 Apr. 10 05:30
2001 Aug. 18 21:30 2001 Aug. 15 23:54
2001 Sep. 30 11:30. . . not clear. . .
2001 Nov. 25 13:30 2001 Nov. 22 22:48
2002 May 25 18:00. . . not clear. . .
2002 Sep. 8 16:30
2002 Sep. 5 16:54
2002 Oct. 1 16:30. . . not clear. . .
2003 Nov. 22 06:50 2003 Nov. 18 08:50
2004 Jul. 28 00:00
2004 Jul. 25 14:54

Notes. Events that can clearly be associated with near-Sun CMEs and agree with the composite velocity profile (Sect. 2.2) have a CME launchtime (near the Sun) mentioned next to them. These events form our final shortlist (shortlist 3). Magnitude: magnitude of FD in vertical direction.
FD onset: time of FD onset in UT. FD minimum: time of FD minimum in UT. MC start: magnetic cloud start time in UT. MCstop: magnetic cloudstop time in UT. CME launch: time at which CME was first observed in the LASCO FOV.

shock, which is approximated as a diﬀusive barrier. Althoughboth the shock and the CME are expected to contribute to the FD,
our treatment seeks to determine which one of them is the dominant contributor at rigidities ranging from 14 to 24 GV. Before
describing the models, we discuss the perpendicular diﬀusion
coeﬃcient.
3.1. Perpendicular diffusion coefficientFig. 2. Velocity profile for the CME corresponding to the 2001
November 24 FD event. The CME was first observed in the LASCO
FOV on 2001 November 22. The solid line shows the first stage governed by LASCO observations Eq. (1), where the CME is assumed tohave a constant deceleration. The dashed line shows the second stage
Eq. (2), where the CME is assumed to experience an aerodynamic dragcharacterized by a constant CD .

Rf is equal to 1 AU. We have used a constant drag coeﬃcient
CD and adjusted its value so that the total travel time thus calculated matches the time elapsed between the first detection of the
CME in the LASCO FOV and its detection as a magnetic cloudnear the Earth. We have retained only those events for which it ispossible to find a constant CD and this criterion is satisfied. We
have also eliminated magnetic clouds that could be associatedwith multiple CMEs. This defines our final shortlist, which wecall shortlist 3. The events that have an entry in the last column
labeled CME launch in Table 1 comprise shortlist 3. We notethat we have adjusted the parameter CD so that the final CME
speed obtained from Eq. (2) is close to the observed magnetic
cloud speed near the Earth. It is usually not possible to find a CDthat will yield an exact match for the velocities and for the total
travel times (e.g., Lara et al. 2011). Figure 2 shows an example of the composite velocity profile (given by Eqs. (1) and (2))
for a representative CME that was first observed in the LASCO
FOV on 2001 November 22, and that resulted in a FD on 2001
November 24.

3. Models for FDs
We apply two diﬀerent models to the FD events in Table 1; thefirst one is the CME-only model, which assumes that the FD
owes its origin only to the CME. The second one is the shockonly model, which assumes that the FD is exclusively due to the

We use an isotropic perpendicular diﬀusion coeﬃcient (D⊥ ) to
characterize the penetration of cosmic rays across large scale, ordered magnetic fields. We envisage a CME, which has a flux rope
structure, propagates outwards from the Sun, driving a shock
ahead of it (see, e.g., Vourlidas et al. 2012). The flux rope CMEshock geometry is illustrated in Fig. 1. The CME sheath region
between the CME and the shock is known to be turbulent (e.g.,
Manoharan et al. 2000) and it is well accepted that it has a significant role to play in determining FDs (Badruddin 2002; Yu
et al. 2010). The isotropic perpendicular diﬀusion coeﬃcient D⊥
characterizes the penetration of cosmic rays through the ordered,compressed large-scale magnetic field near the shock, and acrossthe ordered magnetic field of the flux rope CME. In diﬀusing
across the shock, the cosmic rays are aﬀected by the turbulenceahead of the shock, and in diﬀusing across the magnetic fields
bounding the flux rope CME, the cosmic rays are aﬀected by the
turbulence in the CME sheath region.
The subject of charged particle diﬀusion across field lines in
the presence of turbulence is a subject of considerable research.
Analytical treatments include the so-called classical scattering
theory (e.g., Giacalone & Jokipii 1999, and references therein),and the nonlinear guiding center theory (Matthaeus et al. 2003;
Shalchi 2010) for perpendicular diﬀusion. Numerical treatments
include Giacalone & Jokipii (1999), Casse et al. (2002), Candia& Roulet (2004) and Tautz & Shalchi (2011). For our purposes,
we seek a concrete, usable prescription for the D⊥ that can incorporate as many observationally determined quantities as possible. We find that the analytical fits to extensive numericalsimulations provided by Candia & Roulet (2004), best suit ourrequirements. We note, in particular, that their results not only
reproduce the standard results of Giacalone & Jokipii (1999)
and Casse et al. (2002) but also extend the regime of validity
to include strong turbulence and high rigidities. Our approach
is similar to that of Eﬀenberger et al. (2012), who adopt empirical expressions for the perpendicular diﬀusion coeﬃcients.
It should be mentioned, however, that they allow for the possibility of anisotropic perpendicular diﬀusion. We treat the caseA139, page 3 of 11

A&A 555, A139 (2013)of radial diﬀusion across the largely azimuthal magnetic fields
bounding a flux rope CME structure, and we therefore need only
one (isotropic) perpendicular diﬀusion coeﬃcient (D⊥ ).
In the formulation of Candia & Roulet (2004), the perpendicular diﬀusion coeﬃcient D⊥ is a function of the quantity ρ(which is closely related to the rigidity and indicates how tightly
the proton is bound to the magnetic field) and the level of turbulence σ2 . Our characterization of D⊥ (ρ, σ2 ) follows that of S09,
who adopt the analytical fits to Monte Carlo simulations of particle transport in turbulent magnetic fields given by Candia &Roulet (2004). The quantity ρ is related to the rigidity Rg by
ρ=

Rg
RL
=
Lmax
B0 Lmax(4)

where RL is the Larmor radius and B0 is the strength of therelevant large-scale magnetic field. For the CME-only model,
B0 refers to the large-scale magnetic field bounding the CME,
and for the shock-only model, it refers to the enhanced largescale magnetic field at the shock. In writing second step in
Eq. (4), we have related the Larmor radius to the rigidity Rg by
RL (t) =

Rg
·
B0

(5)

For the CME-only model, we adopt Lmax = 2 R(T ), where R(T )is the radius of the near-Earth magnetic cloud. This is in contrast
with S09, where Lmax was taken to be 106 km, which is the approximate value for the outer scale of the turbulent cascade in
the solar wind. For the shock-only model, on the other hand, we
assume that Lmax is equal to 1 AU.
The turbulence level σ2 is defined (as in Candia & Roulet
2004, and S09) to be
σ2 ≡

Br 2
,
B0 2

(6)

where Br is the fluctuating part of the turbulent magnetic field
and the angular braces denote an ensemble average.
For the sake of completeness, we reproduce the full expression for the isotropic perpendicular diﬀusion coeﬃcient that we
use in this work. It is the same as the one used in S09, and istaken from Candia & Roulet (2004). The diﬀusion coeﬃcientdue to scattering of particles along the mean magnetic field D
is given by ρ 2(1−γ)  ρ 2N
D = c Lmax ρ 2
+
,
(7)
ρ
ρ
σ
where c is the speed of light and the quantities N , γ and ρ areconstants specific for diﬀerent kinds of turbulence. The perpendicular diﬀusion coeﬃcient (D⊥ ) is related to the parallel coeﬃcient (D ) by
D⊥
=
D



ρ ≤ 0.2N⊥ (σ2 )a⊥ , ρ −22 a⊥, ρ > 0.2.
N⊥ (σ )
0.2

(8)

The quantities N⊥ and a⊥ are constants specific to diﬀerent kindsof turbulent spectra. In this work, we assume the Kolmogorov
turbulence spectrum in our calculations. We use N = 1.7, γ =5/3, ρ = 0.20, N⊥ = 0.025, and a⊥ = 1.36 (Table 1, Candia& Roulet 2004). Equation (7) together with Eq. (8) defines theisotropic perpendicular diﬀusion coeﬃcient we use in this work.
A139, page 4 of 11

Fig. 3. An illustration depicting a flux rope CME expanding and propagating away from the Sun. High-energy Galactic cosmic rays diﬀuse
into the CME across its bounding magnetic field.

3.2. CME-only model

The basic features of the CME-only model are similar to the oneused in S09 and here we only highlight the areas where there are
significant diﬀerences from S09. There are practically no highenergy Galactic cosmic rays inside the CME when it starts out
near the Sun. The cosmic rays diﬀuse into it from the surroundings via perpendicular diﬀusion across the closed magnetic fieldlines as it propagates through the heliosphere as shown schematically in Fig. 3. Near the Earth, the diﬀerence between the (relatively lower) cosmic ray proton density inside the CME and thatin the ambient medium appears as the FD. We then obtain an
estimate of the cosmic ray proton density inside the CME produced by the cumulative eﬀect of diﬀusion.
The flux F of protons diﬀusing into the CME at a given timedepends on the isotropic perpendicular diﬀusion coeﬃcient D⊥
and the density gradient ∂Na /∂r, and can be written as
F (cm−2 s−1 ) = D⊥

∂Na
·
∂r

(9)

As mentioned earlier, the D⊥ characterizes diﬀusion across the(largely closed) magnetic fields bounding the CME, and Na isthe ambient density of high energy protons. The total number ofcosmic ray protons that will have diﬀused into the CME after atime T is related to the diﬀusing flux by
T

Ui =

T

A(t)F(t) dt =0D⊥ A(t)
0

∂Na
dt,
∂r

(10)

where A(t) is the cross-sectional area of the CME at a given
time t. According to our convention, the CME is first observed in
the LASCO FOV at t = 0 and reaches the Earth at t = T . The ambient density gradient ∂Na /∂r is approximated by the expression
∂Na
∂r

Na
,
L

(11)

which is significantly diﬀerent from that used in S09, where L
is the gradient lengthscale. Observations of the density gradient lengthscale L exist only for a few rigidities. We use the observations of Heber et al. (2008), who quote a value of L−1 =4.7% AU−1 for 1.2 GV protons. We take this as our reference value. In order to calculate L for other rigidities (in the
14−24 GV range that we use here), we assume that L ∝ R1/3
L .
This is broadly consistent with the observation (De Simone
et al. 2011) that the density gradient lengthscale is only weakly
dependent on rigidity. For a given rigidity, we also need the valueK. P. Arunbabu et al.: High-rigidity Forbush decreasesof L all the way from the Sun to the Earth. In order to calculate this, we recognize that L near the CME/magnetic cloud
will not be the same as its value in the ambient solar wind.
We adopt L ∝ Ba /BMC, where BMC is the large-scale magnetic
field bounding the CME and Ba is the (weaker) magnetic field in
the ambient medium outside the CME. Furthermore, while BMC
varies according to Eq. (12) below, the ambient field Ba of theParker spiral in the ecliptic plane varies inversely with heliocentric distance.
We assume that the magnetic flux associated with the CME
is frozen-in with it as it propagates. In other words, the productof the CME magnetic field and the CME cross-sectional area
remains constant. This is a fairly well-founded assumption (e.g.,
Kumar & Rust 1996; Subramanian & Vourlidas 2007). One cantherefore relate the CME magnetic field B0 (t) at a given time t to
the value BMC measured in the near-Earth magnetic cloud by
B0 (t) = BMC

R(T )
R(t)

2

,

(12)

where R(T ) is the radius of the magnetic cloud observed from the
Earth and R(t) is its radius at any other time t during its passage
from the Sun to the Earth. The CME radius R(t) and R(T ) are
related via Eq. (15) below. We emphasize that the magnetic fieldin Eq. (12) refers to the magnetic field bounding the CME, andnot the ambient magnetic field outside it.
We model the CME as an expanding cylindrical flux rope
whose length increases with time as it propagates outwards. Its
cross-sectional area at time t is
A(t) = 2πL(t)R(t),(13)

where L(t) is the length of the flux-rope cylinder at time t, and isrelated to the height H(t) of the CME above the solar limb via
L(t) = πH(t) .

(14)

We note that Eq. (14) diﬀers from the definition used in S09
by a factor of 2. We assume that the CMEs expand in a selfsimilar manner as they propagate outwards. The three dimensional flux rope fittings to CMEs in the ∼2−20 R field of viewusing SECCHI/STEREO data validate this assumption (e.g.,
Poomvises et al. 2010). The self-similar assumption means thatthe radius of the R(t) of the flux rope is related to its heliocentricheight H(t) by
R(t)
R(T )
=
,
H(t) H(T )(15)where H(T ), the heliocentric height at time T , is =1 AU by definition, and R(T ) is the measured radius of the magnetic cloudfrom the Earth.
As mentioned earlier, we consider a two-stage velocity profile for CME propagation, expressed by Eqs. (1) and (2); this issubstantially diﬀerent from the constant speed profile adopted
in S09.
Using Eqs. (11), (13) and (14) in (10), we get the expression
for the total number of protons inside the CME when it arriveson the Earth
T

Ui =
0

Na
2πL(t)R(t)D⊥dt .
κRL (t)0.33

Fig. 4. Muon flux along the nine directions is shown for the FD on
2001 November 24. The fluxes are shown as percentage deviations frommean values. The solid black lines show the data after applying a lowpass filter (S09). The blue dashed line in the first panel shows the magnetic field observed in-situ by spacecraft. The magnetic field data areinverted (i.e., magnetic field peaks appear as troughs) and are scaled
to fit in the panel. The red dotted line in the middle panel shows Tibet
neutron monitor data scaled down by a factor of 3 to fit in the panel.

(16)

The cosmic ray density inside the CME when it arrives on the
Earth is
Ui
Ni =
,
(17)
πR(T )2 L(T )where L(T ) and R(T ) are the length and cross-sectional radiusof the CME, respectively, at time T , when it reaches the Earth.
When the CME arrives on the Earth, the relative diﬀerence between the cosmic ray density inside the CME and the ambientenvironment is manifested as the FD, whose magnitude M canbe written as
M=Na − Ni ΔN
=
·
Na
Na

(18)

We compare the value of the FD magnitude M predicted by
Eq. (18) with observations in Sect. 4.
An example of an FD event observed in all 9 bins of
GRAPES-3 is shown in Fig. 4. The x-axis is the time in days
starting from 2001 November 1 and the y-axis gives the percentage deviation of the muon flux from the pre-event mean. The
magnitude M of the FD for a given rigidity bin is the diﬀerence
between the pre-event cosmic ray intensity and the intensity at
the minimum of the FD.
3.3. Shock-only model

In this approach, we assume that the FD is caused exclusively by
the shock, which is modeled as a propagating diﬀusive barrier.
The expression for the magnitude of the FD according to thismodel is (Wibberenz et al. 1998)M≡D⊥ aUa − Ushock ΔU
Vsw Lshock
=
=
−1 ,
Ua
Ua
D⊥ a
D⊥ shock(19)

where Ua is the ambient cosmic ray density and Ushock is that
inside the shock, D⊥ a is the ambient isotropic perpendicular diffusion coeﬃcient and D⊥ shock is that inside the shock, Vsw is thesolar wind velocity, and Lshock is the shock sheath thickness. For
each shock event, we examine the magnetic field data from theA139, page 5 of 11

A&A 555, A139 (2013)
Table 2. Minimum χ2 values for the CME-only model fits to
GRAPES-3 data.
Event
2001 April 11
2001 August 17
2001 November 24
2002 September 7
2003 November 20
2004 July 26

Fig. 5. Interplanetary magnetic field and solar wind speed from the day
2001 November 24, The shock sheath thickness is computed by multiplying the time interval inside the dotted lines by the solar wind speed.

ACE and WIND spacecrafts and estimate the shock sheath thickness Lshock to be the spatial extent of the magnetic field enhancement. An example is shown in Fig. 5.
In computing D⊥ a and D⊥ shock we need to use diﬀerent values for the proton rigidity ρ for the ambient medium and in theshock sheath; they are related to the proton rigidity Rg byRg
B0 LshockRgρshock = shock,
B0
Lshockρa =adistance (in units of R ) at which CME was first observed in
LASCO FOV and Rlast is the distance at which the CME waslast observed in LASCO FOV. The quantity Vexp is the speedof CME at Rlast (in km s−1 ) and ai is the acceleration of CMEin the LASCO FOV (in m s−2 ). The quantity CD is the (constant) dimensionless drag coeﬃcient used for the velocity profile(Sect. 2.2). The quantities MC start and MC end denote the startMCand end times of the magnetic cloud in UT. The quantity Vsw
is solar wind speed at the Earth (in km s−1 ) just ahead of thearrival of the magnetic cloud, and RMC is the radius of the magnetic cloud (in km). The quantity BMC is the peak magnetic field
inside the magnetic cloud (in nT). The quantity T total is the SunEarth travel time (in h) taken by the CME to travel from Sun to
Earth. The quantity Shock arrival denotes the time (in UT) when
the shock is detected near the Earth. The quantities Ba and Bshock
represent the magnetic fields (in nT) in the ambient solar wind
and inside the shock sheath region, respectively (see Fig. 5 forshock
an example). The quantity Vsw
represents the near-Earth shock−1
speed in km s .
Table A.1 contains details of the FDs associated with eachof the CMEs in the final shortlist. The magnitude of the FD in agiven rigidity bin is the diﬀerence between the pre-event intensity of the cosmic rays and the intensity at the minimum of the
FD. It also contains the onset and the time of minimum, and themagnitude of the decrease in each bin (together with the corresponding cutoﬀ rigidity) for each of the FD events in our final
shortlist.

(20)
(21)

where Ba0 is the ambient magnetic field and Bshockis the magnetic
0
field inside the shock sheath.

4. Results
In this section we first describe various parameters needed for
the CME-only and the shock-only models that are derived fromobservations. Using these parameters, we examine whether thenotion of cosmic ray diﬀusion is valid for each model. Using theobservationally determined parameters, we can determine whichof the two models best reproduces the observed FD magnitudein each rigidity bin.
4.1. Observationally derived parameters

Table A.2 contains the observationally determined parameters
for each of the CMEs and their corresponding shocks in the final
shortlist (Table 1).
The quantity First obs denotes the time (in UT) when the
CME was first observed in the LASCO FOV, while Rfirst is theA139, page 6 of 11

χ2
11.1
1.96
2.46
25.5
3.66
27.5

4.2. Fitting the CME-only and shock-only models
to multi-rigidity FD data

Using the observational parameters listed in Table A.2, wehave computed the magnitude of the FD using the CME-only(Sect. 3.2) and shock-only models (Sect. 3.3). The only free parameter in our model is the ratio of the energy density in the
random magnetic fields to that in the large scale magnetic field
σ2 ≡ Bturb 2 /B0 2 . Figure 6 shows the best fits of the CMEonly model to the multi-rigidity data. The only free parameterin the model is σ2 ≡ Bturb 2 /B02 , and the best fit is chosen byminimizing the χ2 with respect to σ2 . For each FD event, the∗ symbols denote the observed FD magnitude for a given rigidity bin. The dashed line denotes the FD magnitude predicted by
the CME-only model. We define the chi-square statistic as (Ei − Di )2
χ2=
,
(22)
vari
i
where Ei is the value predicted by the theoretical model, Di is
the corresponding GRAPES-3 data point, and vari is the variancefor the corresponding data points. The χ2 values obtained after
minimizing with respect to σ2 are listed in Table 2.
The entries in the second column σMC in Table 3 denote thesquare roots of the turbulence parameter σ2 that we have used forK. P. Arunbabu et al.: High-rigidity Forbush decreases

Fig. 6. FD magnitude observed with GRAPES-3 (∗ symbols). The dashed line is obtained using the CME-only model.
Table 3. Turbulence levels in the sheath region required by the models.
Event
2001 April 11
2001 August 17
2001 November 24
2002 September 7
2003 November 20
2004 July 26

CME-only model
σMC
9.4%
13%
28%
13%
6.7%
46%

shock-only modelσShock
100%
180%
400%
100%
400%
200%

the model fits for each event. These values represent the level of
turbulence in the sheath region immediately ahead of the CME,
through which the cosmic rays must traverse in order to diﬀuse
into the CME. By comparison, the value of σ for the quiescentsolar wind ranges from 6 to 15% (Spangler 2002). Evidently,
the CME-only model implies that the sheath region ahead of

the CME is only a little more turbulent than the quiescent solar wind, except for the 2004 July 26 event, where the speedof CME at the Earth was much higher than that for the otherevents.
We have carried out a similar exercise for the shock-onlymodel (Sect. 3.3). For each event, we have used the observationally obtained parameters pertaining to the shock listed inTable A.2. Since this model needs the turbulence levels in boththe ambient medium and the shock sheath region to be specified, we have assumed that the turbulence level inside the shock
sheath region is twice that in the ambient medium. We find that
it is not possible to fit the shock-only model to the multi-rigidity
data using values for the turbulence parameter that are reasonably close to that in the quiescent solar wind. For each event, thecolumn labeled σShock in Table 3 denotes the turbulence level inthe shock sheath region that is required to obtain a reasonable
fit to the data. Clearly, these values are an order of magnitude
higher than those observed in the quiet solar wind.
A139, page 7 of 11

A&A 555, A139 (2013)

Fig. 7. f0 ≡ RL /R versus distance as a CME propagates from the Sun to the Earth. The dashed and continuous lines represent 24 GV and
12 GV protons, respectively.

4.3. RL /RCME for CME-only model

Kubo & Shimazu (2010) have simulated the process of cosmic ray diﬀusion into an ideal flux rope CME in the presence of MHD turbulence. They find that, if the quantity
f0 (t) ≡ RL (t)/R(t) is small, cosmic ray penetration into the flux
rope is dominated by diﬀusion via turbulent irregularities. Othereﬀects such as gradient drift due to the curvature of the magnetic
field are unimportant under these conditions. Figure 7 shows
the quantity f0 (t) ≡ RL (t)/R(t) for 12 and 24 GV protons, foreach of the CMEs in our final shortlist (Table 1). The Larmor
radius RL (t) is defined by Eqs. (5) and (12) and the CME radius R(t) is defined in Eq. (15). Clearly, f0  1 all through the
Sun-Earth passage of the CMEs, and this means that the role of
MHD turbulence in aiding penetration of cosmic rays into theflux rope structure is expected to be important.

5. Summary
Our main aim in this work is to determine whether FDs due tocosmic rays of rigidities ranging from 14 to 24 GV are caused
primarily by the CME, or by the shock associated with it. We
examine this question in the context of multi-rigidity FD datafrom the GRAPES-3 instrument. We use a carefully selected
sample of FD events from GRAPES-3 that are associated withboth CMEs and shocks.
We consider two models: the CME-only model (Sect. 3.2)
and the shock-only model (Sect. 3.3). In the CME-only model,
we envisage the CME as an expanding bubble bounded by
A139, page 8 of 11

large-scale magnetic fields. The CME starts out near the Sun
with practically no high energy cosmic rays inside it. As it travel
towards the Earth, high-energy cosmic rays diﬀuse into the CME
across the large-scale magnetic fields bounding it. The diﬀusion
coeﬃcient is a function of the rigidity of the cosmic ray particles as well as the level of MHD turbulence in the vicinity of theCME (the sheath region). Despite the progressive diﬀusion ofcosmic rays into it, the cosmic ray density inside the CME is still
lower than the ambient density when it reaches the Earth. When
the CME engulfs the Earth, this density diﬀerence causes the FD
observed by cosmic ray detectors. In the shock-only model, we
consider the shock as a propagating diﬀusive barrier. It acts as anumbrella against cosmic rays, and the cosmic ray density behindthe umbrella is lower than that ahead of it.
We have obtained a list of FD events observed by the
GRAPES-3 instrument using the shortlisting criteria describedin Sect. 2. For each of these shortlisted events, we have used observationally derived parameters listed in Table A.2 for both themodels. The only free parameter was the level of MHD turbulence (defined as the square root of the energy density in the turbulent magnetic fluctuations to that in the large-scale magnetic
field) in the sheath region.

6. Conclusions
Figure 6 shows the results of the CME-only model fits to multirigidity data for each of the shortlisted events. For the shock-onlymodel, we use the turbulence level in the shock sheath region
as the free parameter. Table 3 summarizes the values of theseK. P. Arunbabu et al.: High-rigidity Forbush decreases

turbulence levels that we have used for each of the FD events inthe final shortlist. These values may be compared with the estimate of 6 to 15% for the turbulence level in the quiescent solar
wind (Spangler 2002). We thus find that a good model fit using
the CME-only model requires a turbulence level in the sheathregion that is typically only a little higher than that in the quiescent solar wind, which is generally consistent with observations. On the other hand, a good fit using the shock-only model
demands a turbulence level in the shock sheath region that isoften an order of magnitude higher than that in the quiet solar
wind, which is somewhat unrealistic. The results summarized inTable 3, imply that, for FDs involving protons of rigidities ranging from 14 to 24 GV, the CME-only model is a viable one, while
the shock-only model is not. Given the remarkably good fits tomulti-rigidity data (Fig. 6), the reasonable turbulence levels inthe sheath region demanded by the CME-only model (Table 3)
and because the FD minima usually occur well within the magnetic cloud (Table A.1), we conclude that CMEs are the dominant contributors to the FDs observed by the GRAPES-3 experiment.
Acknowledgements. K.P. Arunbabu acknowledges support from a Ph.D. studentship at IISER Pune. P. Subramanian acknowledges partial support from the
RESPOND program administered by the Indian Space Research Organization.
We thank Alejandro Lara for useful discussions and the referee K. Scherer forseveral critical and helpful suggestions. We thank D. B. Arjunan, A. Jain, the late
S. Karthikeyan, K. Manjunath, S. Murugapandian, S. D. Morris, B. Rajesh, B. S.
Rao, C. Ravindran, and R. Sureshkumar for their help in the testing, installation,and operating the proportional counters and the associated electronics and during data acquisition. We thank G. P. Francis, I. M. Haroon, V. Jeyakumar, and K.
Ramadass for their help in the fabrication, assembly, and installation of various
mechanical components and detectors.

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Pages 10 to 11 are available in the electronic edition of the journal at http://www.aanda.org

A139, page 9 of 11

A&A 555, A139 (2013)

Appendix A: Tables
Table A.1. Derived parameters of FD for events.
1 FD onset times in UT 2001 Apr. 11

2001 April 11
Shock
Magnetic Cloud

ArrivalStart: 2001 Apr. 11 14:06: 2001 Apr. 11 23:00

2 FD minimum times in UT 2001 Apr. 12

End: 2001 Apr. 12 18:00

Quantity

NW

N

NE

W

V

E

SW

S

SE

FD Magnitude (%)
Cutoﬀ Rigidity (GV)
FD Onset (UT)
FD minimum (UT)

1.02
15.5
12:57
19:00

1.12
18.7
13:55
19:00

0.91
24.0
16:04
19:00

1.38
14.3
11:16
17:00

1.40
17.2
12:00
18:00

1.05
22.4
12:57
18:00

1.36
14.4
08:24
14:00

1.29
17.6
10:20
15:00

0.93
22.4
12:28
16:00

2001 August 17

1 FD onset times in UT 2001 Aug. 17

2 ∗ FD onset times in UT 2001 Aug. 16: 2001 Aug. 17 11:00: 2001 Aug. 18 00:00

3 FD minimum times in UT 2001 Aug. 18

Shock
Magnetic Cloud

ArrivalStart

Quantity

NW

N

NE

W

V

E

SW

S

FD Magnitude (%)
Cutoﬀ Rigidity (GV)
FD Onset (UT)
FD minimum (UT)

1.17
15.5
04:19
4:00

1.12
18.7
01:55
3:00

0.83
24.0
01:12
2:00

0.97
14.3
23:17∗
6:00

1.03
17.2
22:34∗
5:00

0.79
22.4
22:05∗
5:00

1.12
14.4
00:00
23:00

1.07
17.6
23:31∗
22:00

End

1

2001 November 24: 2001 Aug. 18 21:30

2

FD onset times in UT 2001 Nov. 24: 2001 Nov. 24 06:00: 2001 Nov. 24 17:00

SE
0.80
22.4
23:17∗
20:00

FD minimum times in UT 2001 Nov. 25

Shock
Magnetic Cloud

ArrivalStart

End: 2001 Nov. 25 13:00

Quantity

NW

N

NE

W

V

E

SW

S

SE

FD Magnitude (%)
Cutoﬀ Rigidity (GV)
FD Onset (UT)
FD minimum (UT)

1.42
15.5
03:07
17:00

1.34
18.7
03:21
15:00

0.94
24.0
03:07
16:00

1.67
14.3
04:05
14:00

1.56
17.2
03:21
15:00

1.16
22.4
02:52
17:00

1.34
14.4
04:05
15:00

1.36
17.6
03:07
16:00

1.10
22.4
01:24
19:00

1 FD onset times in UT 2002 Sep. 7

2002 September 7
Shock
Magnetic Cloud

ArrivalStart: 2002 Sep. 7 14:20: 2002 Sep. 7 17:00

End

2 FD minimum times in UT 2002 Sep. 8: 2002 Sep. 8 16:30

Quantity

NW

N

NE

W

V

E

SW

S

SE

FD Magnitude (%)
Cutoﬀ Rigidity (GV)
FD Onset (UT)
FD minimum (UT)

0.41
15.5
17:03
15:00

0.59
18.7
17:17
14:00

0.63
24.0
16:05
14:00

0.89
14.3
14:52
13:00

0.97
17.2
14:52
13:00

0.83
22.4
15:07
14:00

1.08
14.4
15:50
15:00

1.07
17.6
16:19
16:00

0.84
22.4
17:03
16:00

1 FD onset times in UT 2003 Nov. 20

2003 November 20
Shock
Magnetic Cloud

3 The ∗∗ FD onset times in UT 2003 Nov. 21

ArrivalStart: 2003 Nov. 20 07:30: 2003 Nov. 20 10:06

End

2 The ∗ FD onset times in UT 2003 Nov. 19
4 FD minimum times in UT 2003 Nov. 24: 2003 Nov. 21 00:24

Quantity

NW

N

NE

W

V

E

SW

S

SE

FD Magnitude (%)
Cutoﬀ Rigidity (GV)
FD Onset (UT)
FD minimum (UT)

0.95
15.5
21:22 ∗
5:00

0.93
18.7
08:10∗∗
4:00

0.81
24.0
02:53∗∗
2:00

1.19
14.3
01:55
4:00

1.16
17.2
10:48
4:00

0.97
22.4
20:38
4:00

1.17
14.4
06:58
3:00

1.20
17.6
10:19
3:00

0.93
22.4
15:07
2:00

1 FD onset times in UT 2004 Jul. 26

2004 July 26
Shock
Magnetic Cloud

ArrivalStart: 2004 Jul. 26 22:20: 2004 Jul. 27 02:00

End

2 FD minimum times in UT 2004 Jul. 27: 2004 Jul. 27 24:00

Quantity

NW

N

NE

W

V

E

SW

S

SE

FD Magnitude (%)
Cutoﬀ Rigidity (GV)
FD Onset (UT)
FD minimum (UT)

2.06
15.5
14:24
10:00

2.04
18.7
15:22
11:00

1.67
24.0
17:17
13:00

2.40
14.3
14:10
10:00

2.12
17.2
15:36
11:00

1.62.
22.4
18:00
13:00

1.77
14.4
16:05
12:00

1.67
17.6
18:29
14:00

1.40
22.4
20:38
15:00

Notes. For each event, first row: magnitude of FD (FD magnitude), second row: cutoﬀ rigidity, third row: FD onset time, fourth row: FD minimum
time. The units in which each quantity is expressed is given in parentheses in the first column.

A139, page 10 of 11

K. P. Arunbabu et al.: High-rigidity Forbush decreases
Table A.2. Observed parameters of CME & Shock for diﬀerent events.
Event
2001 Apr. 11
2001 Aug. 17
2001 Nov. 24
2002 Sep. 7
2003 Nov. 20
2004 Jul. 26
CME detailsaFirst obs. ( UT) 2001 Apr. 10 05:30 2001 Aug. 15 23:54 2001 Nov. 22 22:48 2002 Sep. 5 16:54 2003 Nov. 18 8:50 2004 Jul. 25 14:54
b
Rfirst (R )
2.84
3.38
4.77
4.12
6.3
4.22
c
Rlast (R )
18.1
25.9
25.9
17.0
27.5
21.9
d
Vexp (km s−1 )
2880
1410
1370
1860
1650
1370
e
ai (m s−2 )
211
–31.7
–12.8
43.0
–3.29
7.0
f
CD
0.325
0.163
0.09
0.312
0.333
0.016
g
MC start (UT)2001 Apr. 11 23:00 2001 Aug. 18 00:00 2001 Nov. 24 17:00 2002 Sep. 7 17:00 2003 Nov. 20 10:06 2004 Jul. 27 2:00
h
MC end (UT)2001 Apr. 12 18:00 2001 Aug. 18 21:30 2001 Nov. 25 13:00 2002 Sep. 8 16:30 2003 Nov. 21 00:24 2004 Jul. 27 24:00
i MC
Vsw (km s−1 )
725
600
730
544
750
900
j
RMC (km )2.48 × 107
2.32 × 107
2.63 × 107
2.30 × 107
1.89 × 107
3.56 × 107
k
BMC (nT)
34.5
25.6
20
22.9
50
25.3
l
T total (h)
42.1
44.9
41.1
48.9
42.1
35.7
Shock
Shock arrival (UT) 2001 Apr. 11 14:06 2001 Aug. 17 11:00 2001 Nov. 24 6:00 2002 Sep. 7 14:20 2003 Nov. 20 7:30 2004 Jul. 26 22:20
m a
B (nT)
4.5
5
5
5.8
7
5
n shock
B
(nT)
32.5
33
41.5
23
26.1
o shockVsw (km s−1 )
670
501
948
550
893
Notes. (a) First obs.: time in UT when the CME was first observed. (b) Rfirst : distance in (R ), where CME was first observed. (c) Rlast : distance in(R ), where the CME was last observed in the LASCO FOV. (d) Vexp : speed of CME in (km s−1 ) at Rlast . (e) ai : acceleration of CME in LASCO FOV
in units of (m s−2 ). ( f ) CD : the constant dimensionless drag coeﬃcient used for the velocity profile (Sect. 2.2). (g) MC start: Magnetic cloud startMCtime in UT. (h) MC end: Magnetic cloud end time in UT. (i) Vsw: solar wind speed in (km s−1 ) at Earth during the arrival of the magnetic cloud.
( j)(k)
RMC : radius of magnetic cloud in (km ). BMC : magnetic field inside the magnetic cloud (nT). (l) T total : the Sun-Earth travel time in h for theshock
CME. (m) Ba: magnetic field in the ambient solar wind (in nT). (n) Bshock : magnetic field inside the shock sheath region (in nT). (o) Vsw: near-Earth−1
shock speed (km s ).

A139, page 11 of 11